The DNA data storage based on the marker-LDPC code is designed, which can correct insertions/deletions/ substitutions and recover the stored information accurately. In this system, the data was mapped to the LDPC codeword, and then the known marker was inserted into it to construct the concatenated code, which was subsequently converted to the DNA sequence by employing the quadratic encoding method. Next, the DNA sequence was synthesized and stored. Finally, we extracted the DNA for sequencing, and then the stored information was recovered through the decoding based on the weighted Levenshtein distance. Experiment results show that the reliable DNA storage can be achieved with the marker-LDPC code.